# Clock wise (time)

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Purpose

In this unit students explore hours, half-hours, and quarter-hours using analogue and digital clocks.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Specific Learning Outcomes
• Tell time to the hour, half and quarter hour using analogue clocks.
• Tell time to the hour, half hour and quarter hour using digital clocks.
• Solve time problems involving hours, half and quarter hours.
Description of Mathematics

In the curriculum, students' experiences with time are focused in two areas: duration and telling time. This unit focuses on learning to read and tell the time

Telling time allows students to develop an understanding of the size of the units of time (hours, minutes, seconds, milliseconds). This includes being able to estimate and measure using units of time.

Clocks are common instruments for measuring time. However, learning to tell the time is more about the skill of learning to read a dial-type instrument than about measuring time. Learning to use an analogue clock is a challenging skill to teach as the two hands of the clock have distinctly different actions and functions. The small hand indicates the approximate time to the nearest hour, and the big hand indicates the minutes after or before an hour. When we look at the big hand we focus on where it is pointing.  When we look at the small hand we look at how far it has moved around the clock or how far it has to get to back to the top.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to additionally support or challenge students include:

• using a one-handed (hour-hand only) clock to support students read the hour hand with reasonable accuracy (e.g. “it’s about 7 o’clock”, “it’s about halfway between 2 o’clock and 3 o’clock”)
• pairing students so that they can (1) be supported, and (2) offer support to others, as they solve the time problems
• working with students to master hour and half-hour understanding, before introducing quarter-hour times
• providing diagrams and models of clocks for students to use, refer to, and fold back to
• asking students to work out problems with or without the aid of materials
• reducing the number of problems that need to be completed
• providing opportunities for students to make up their own time problems
• providing opportunities for more knowledgeable students to explore other times (e.g. ten minutes to, twenty minutes past, a third of an hour, two thirds of an hour until).

The context for this unit can be adapted to suit the interests and experiences of your students. While the focus is on telling the time, the problems can be related to the activities that your students engage with at school and in the community.

Te reo Māori kupu such as he aha te taima? (what is the time?) could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to time that they use at home.

Required Resource Materials
• Resources to be used in creating a mind map (e.g. a graphic organiser)
• Thin card or card circles (to make clock face and hands)
• Split pins
• Analogue clocks (without a second hand and with the facility to change the time easily)
• Digital alarm clocks
• Time Diary - to send home
Activity

#### Session 1: Analogue time

1. Begin by brainstorming and listing the words we use to talk about time. For example: 5 o’clock, quarter or half past/to, six thirty, hours, minutes and seconds.
2. Explain to the students that there are different ways to describe time. Today they are going to explore one way - analogue clocks.
3. Show an analogue clock and discuss the face, drawing out the students' experiences with clocks and time.
What can you tell me about the face?
What numbers are there? Why is there nothing above 12?
How are the numbers arranged? Why?
Tell me about the clocks that you have at home.
What is the biggest clock you have ever seen?
When do you get up?
When do you go to school?
4. Have each student construct an analogue clock. Model the following process for students and support them to each construct one.
• Draw around an object to make a circle of light card or give each student a cut circle of card.
• Fold the circle in half and half again and colour each quarter a different colour – this helps reinforce the concept of quarters and halves.
• Draw numbers onto the clock-face, beginning by placing the 12, 3, 6, and 9 on the ¼ “lines”. Discuss their position.

#### Session 2: Analogue time

1. As a class, discuss times of the day when common events happen and have the students model these times on the analogue clocks they have made. At first focus on hours, e.g. wake up at 7 o’clock, school starts at nine o’clock; lunch is at twelve o’clock; home time is three o’clock. Begin constructing a mind map recording these times (it should have space to record the events that occur, in students' lives, on the hour, and on the half and quarter hour).
2. Ensure that the students understand that the small hand indicates the hour time. Using a clock with only an hour-hand helps students focus on its position at different times. You can do this by adding only the hour-hand to the clock constructed in session 1. Discuss that when the hand is pointing exactly to a number it is an o’clock time.  For example, when it is pointing to the 3 it is 3 o’clock. When it is half-way between the 3 and the 4 it will be close to half-past 3.
3. Introduce the role of the minute-hand by looking at a clock with both hands or by adding the large-hand to the clock created in session 1.
4. Ask "Why does the big hand point to the top with all of the o’clock times?”. Look for students to recognise that the big hand indicates how many minutes have passed since the o’clock time and with hour times “0” minutes have passed.
5. Next discuss the events that occur on the half-hours, e.g. playtime is at half past ten, bed-time is half past seven. Ask students to think about their lives outside school (e.g. dinner is at half past 6). Continue to add to the mind map.
6. Display 1/2 past 10 on a clock, and tell the students that the clock shows 1/2 past time. Ask students to describe the position of the small and big hands.
• Why does the big hand point to the 6?  Check that students see  the relationship between 1/2 of the circle and the position of the big hand pointing to the 6.
• What is the small hand pointing to?  Check that students understand that the small hand has now moved and is half-way between the 10 and the 11.
7. Ask the students to show ½ past 3 on their clocks. As a class, discuss the placement of the hands.
8. Discuss the events that occur on the quarter-hours. Show the quarter-past times identified in discussion on the clock, and ask students to show the time on their own clocks. Continue to add to the mind map.
9. Ask students to record some of their favourite/important times of the day and show these times on their clocks. They could do this with a partner, before sharing one favourite time with the whole class.

#### Session 3: Analogue time

1. Pose several problems involving time (to hours, half-hours, and quarter-hours). Place these problems on cards stationed around the room and have the students work with a buddy and their analogue clock to solve them and record their answers. Alternatively, you could work with the whole class on some of these problems, before allowing more confident students to work at the stations independently. Some students may want to stay and work with the teacher in a more guided fashion.

You could frame all of these problems in a context that is more relevant to your students (e.g. times related to a school trip or to the school day).

• Arni went swimming at 4 o’clock and got out of the pool at five o’clock. How long did he swim for?
• If it takes a quarter of an hour to walk to school from home, how long will it take to walk to school and back home again?
• Laura had an appointment at the dentist at half past three. She didn’t arrive until 4 o’clock. How late was she?
• The movie started at 6 o’clock and finished at half past seven. How long was the movie?
• Muffins take half an hour to cook. If a batch of muffins goes into the oven at half past five what time will they be ready?
1. Gather as a class, discuss the problems, and the solutions. Identify any misconceptions and either address them now, or use them to plan a short review session for the start of the next session.

#### Session 4: Digital Time

1. Review what is known about analogue time.
2. Have the students carefully examine a digital clock and count the number of minutes in each hour. Establish that there are 60 minutes in each hour, and 30 minutes in half an hour. This is also a good opportunity to practice skip-counting with fives.
3. Establish with the students that the first number of the digital clock shows the hour and the second number shows the number of minutes past that hour.
4. Challenge the students by asking them how they think the digital clock would show times that they are familiar with on an analogue clock e.g. nine o’clock (start of school), half past ten (play time), and quarter past ten (brain break).
5. Reinforce the fact that half an hour is thirty minutes, therefore digital times ending in 00 are the same as o’clock and times ending in 30 are the same as half past. This means that times ending in 30 (half of a half) is the same as quarter past. Since 30 + 15 = 45, times ending in 45 are the same as quarter to.
6. Show the students o’clock, half-past, and quarter-past times on an analogue clock.  Ask them to write the equivalent digital time.
7. List some of the students’ favourite TV programmes and have the students record the digital times these programmes come on. Look at a TV guide to confirm the times that they have recorded. There might be a context that is more relevant to your students (e.g. the time of sports games or matches, bus timetables). Choose a context that is meaningful and current.

#### Session 5: Digital Time Problems

1. Pose several problems involving time (to hours, half-hours, and quarter-hours). Place these problems on cards stationed around the room and have the students work with a partner to solve them and record their answers. Alternatively, you could work with the whole class on some of these problems, before allowing more confident students to work at the stations independently. Some students may want to stay and work with the teacher in a more guided fashion.

You could frame all of these problems in a context that is more relevant to your students (e.g. times related to a school trip or to the school day).

• Sally went to play netball at 4.00 and came home at 5.30. How long was she away?
• If it takes 30 minutes to walk to the beach from home, how long will it take to walk to the beach and back home again?
• Laura had an appointment at the doctor at 2.30. She didn’t arrive until 3.00. How late was she?
• Hine’s TV programme started at 7.15 and finished at 8.30. How long was the programme?
• Mark went to his grandma’s at 2.00 and stayed there for 6 hours. What time did he leave?
• Potatoes take 30 minutes to boil. If Mum wants the potatoes to be ready by 5.30, when must she put them in the boiling water?
1. Gather as a class, discuss the problems, and the solutions. Identify any misconceptions and either address them now, or use them to plan a short review session for the start of the next session.

#### Session 6: Mixed Time

1. Review what is known about analogue and digital time.
2. Divide the class into two groups. One of these is the analogue group and the other the digital group. Give each group  digital or analogue clocks to use.
3. Let the analogue group choose a time (involving hours, half-hours, or quarter-hours). Get the digital group to show that time on their clock.
4. Then let the digital group choose a time and ask the analogue group to show it on their clock. Repeat this a few times.
5. Choose any time. Ask questions like
Show me the time in half an hour?
What will be the time 3 hours from now?
What was the time 30 minutes ago?
What will be the time in 15 minutes?
What was the time three half hours ago?
6. Get the groups to make up their own problems like this and like the ones we used earlier. Allow the students to ask each other the questions. Get the students to draw their answers using drawings of both an analogue clock and a digital clock.
7. Ask the students to tell you the main times of the day (when school starts, play time, lunchtime, etc.). Get them to draw these in both analogue and digital formats. Put a selection of their drawings on the wall to refer to later.
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